The precise estimate of a projectile trajectory parameters expected in military applications, space travel, rescue and recovery missions, evacuation warnings, games and hobbies, etc. is a challenging task requiring exact analysis of the three-dimensional projectile flight. Currently existing to it solutions are rather complicated and therefore inconvenient. As cited in U.S. Pat. No. 3,748,440 solutions to two dimensional non-linear differential equations are developed in inertial coordinate systems where integrations are performed to obtain X and Y coordinates associated with Latitude and Longitude. Geometric Line of Sight angles is used in U.S. Pat. No. 6,262,680 B1 to track the target in inertial coordinate system. In U.S. Pat. No. 7,605,747 B1 position and velocity vectors are referenced to a non-inertial reference frame such as Earth Centered Earth Fixed (ECEF) when positional registration bias state vector δX represents the sensor position with respect to the ECEF coordinates. Other publications include introduction of either extra degrees of freedom (Burnett, 1962) in order to describe motion in orthogonal two dimensional planes, or consideration of specific initial conditions (Kashiwagi, 1968), or synchronous geo-satellite (Isaacson et al., 1996) utilizing Kalman Filter algorithm, or algorithm (Siouris, 2004) associated with projectile coordinate along its track. Simple solutions from two technical articles found in the websites are just referring to the Coriolis force to proximate the deviation from estimated locations (https://www.phas.ubc.ca/˜berciu/TEACHING/PHYS206/LECTURES/FILES/coriolis.pdf and http://www.marts100.com/projectile.htm).
Lastly, programmed in MATLAB the process of reverse conversion of Sensor Target Measurements into ECEF coordinates allows predicting Sensor Target Measurements at impact location of projectile and enables the radar to direct its beam to the location (I-295 to I-312, DTFA01-88-c-00042, CDRL-EN25, Change 2, Volume I, 6 Sep. 1991).
General and precise solution to the complex problem of a projectile motion would create the grounds for designing a new device highly efficient for any application related to a projectile flight on any planet.